How to loop animation
First of all make sure that the pose of your objects first keyframe is the same as the one of the last keyframe in the period you want to loop. This can be done by duplicating the first column of keyframes in the Dope Sheet and moving it to the end of the period.

Here are some ways to loop:


at the Timeline: just set the end of your playback/rendering range to the last keyframe and play the result in a loop
in the Dope Sheet: duplicate all keyframes ShiftD and move them after your existing
in the Graph Editor: use loop modifiers for everything animated


Here`s an example using the first method